AsyncThrowsTest.cs

static async Task FailsAsync(bool shouldFail)
{
    if (shouldFail)
        throw new ApplicationException("Custom exception.");

    await Task.CompletedTask;
}

static Task Fails(bool shouldFail)
{
    if (shouldFail)
        throw new ApplicationException("Custom exception.");

    return Task.CompletedTask;
}

static void Main(string[] args)
{
    try
    {
        var t = FailsAsync(true);
        //var t = Fails(true);

        Console.WriteLine("FailsAsync() doesn't fail here.");
    }
    catch (Exception ex)
    {
        Console.WriteLine("Fails() fails here.");

        Console.WriteLine(ex.ToString());
    }
}